#include <algorithm>
#include <cmath>
#include <numeric>
#include <vector>
using int64 = long long;
std::vector<int64> mosaic(std::vector<int> X, std::vector<int> Y, std::vector<int> T, std::vector<int> B, std::vector<int> L, std::vector<int> R) {
const int n = X.size();
std::vector mp_x(6, std::vector<bool>(n + 6));
std::vector mp_y(n + 6, std::vector<bool>(6));
auto set = [&](int x, int y, int v) {
if (x <= 5) mp_x[x][y] = v;
if (y <= 5) mp_y[x][y] = v;
return v;
};
auto get = [&](int x, int y) {
return x <= 5 ? mp_x[x][y] : mp_y[x][y];
};
for (int i = 0; i < n; ++i) {
set(0, i, X[i]), set(i, 0, Y[i]);
}
int min = std::min(-4, 2 - n), max = std::max(4, n - 2);
std::vector<int> marked(std::max(9, 2 * n - 3));
for (int i = 1; i <= 5; ++i) {
for (int j = 1; j < n; ++j) {
marked[i - j - min] = set(i, j, !get(i - 1, j) && !get(i, j - 1));
marked[j - i - min] = set(j, i, !get(j - 1, i) && !get(j, i - 1));
}
}
auto get_pt = [&](int x, int y) -> int {
return (x <= 5 or y <= 5) ? get(x, y) : marked[x - y - min];
};
std::vector prefxs(6, std::vector<int>(n)), prefys(6, std::vector<int>(n));
for (int i = 0; i <= 5; ++i) {
for (int j = 0; j < n; ++j) {
prefxs[i][j] = get_pt(i, j);
prefys[i][j] = get_pt(j, i);
}
std::partial_sum(prefxs[i].begin(), prefxs[i].end(), prefxs[i].begin());
std::partial_sum(prefys[i].begin(), prefys[i].end(), prefys[i].begin());
}
auto prefx = [&](int x, int y1, int y2) {
return prefxs[x][y2] - (y1 == 0 ? 0 : prefxs[x][y1 - 1]);
};
auto prefy = [&](int y, int x1, int x2) {
return prefys[y][x2] - (x1 == 0 ? 0 : prefys[y][x1 - 1]);
};
struct adv {
std::vector<int> marked;
std::vector<int64> pref, prefa;
int n;
adv(std::vector<int> marked) : n(marked.size()), marked(marked), pref(marked.size()), prefa(marked.size()) {
for (int64 i = 0; i < marked.size(); ++i) {
prefa[i] = (i + 1) * marked[i];
}
std::partial_sum(prefa.begin(), prefa.end(), prefa.begin());
std::partial_sum(marked.begin(), marked.end(), pref.begin());
}
int64 querys(int l, int len) {
return pref[l + len - 1] - pref[l - 1];
}
int64 query(int l, int len) {
int r = l + len - 1;
return prefa[r] - prefa[l - 1] - l * (pref[r] - pref[l - 1]);
}
int64 queryr(int l, int len) {
return query(n + len - l - 2, len);
}
};
adv l(marked);
std::reverse(marked.begin(), marked.end());
adv r(marked);
std::vector<int64> ans(T.size());
for (int i = 0; i < T.size(); ++i) {
int x1 = T[i], y1 = L[i], x2 = B[i], y2 = R[i];
while (x1 <= x2 and x1 <= 5) {
ans[i] += prefx(x1++, y1, y2);
}
if (x1 > x2) {
continue;
}
while (y1 <= y2 and y1 <= 5) {
ans[i] += prefy(y1++, x1, x2);
}
if (y1 > y2) {
continue;
}
int steps = x2 - x1 + 1;
int len = y2 - y1 + 1;
int mid = std::min(steps, len);
int gap = std::abs(steps - len);
int beg = x1 - y2 - min;
ans[i] += l.query(beg, mid - 1) + mid * l.querys(beg + mid - 1, gap + 1) + r.queryr(beg + gap + 1, mid - 1);
}
return ans;
}
